Topology construction, the initial step of the topology control, is an important technique for a wireless ad hoc network to be energy-efficient. In , we have proposed to use the relative neighborhood graph (RNG) to obtain an RNG-based topology in which the transmission ranges between wireless nodes are reduced. Then, among the RNG-based topology, we proposed a green clustering algorithm (GCA) to organize the wireless nodes into a clustered network topology. In this paper, we further analyze the energy consumption in exchanging data packets and cluster maintenance messages. Simulation results confirm that the proposed RGCA (i.e., combining the RNG and GCA) provides a way to construct an energy-efficient cluster topology for wireless ad hoc networks.